1. Field of the Invention
The invention relates to micromechanical elements. Especially, the invention relates to controlling micromechanical elements such as micromechanical capacitive or galvanic switches or microrelays, micromechanical optical switches, bi-stable tunable capacitors or capacitor banks, or any other bi-stable or multi-state micromechanical actuators.
2. Micromechanical Elements
In microelectronics the trend is towards a higher level of integration. The same is happening in micromechanics as well. Consequently, micromechanical elements designated especially for microelectronic purposes need to be more highly integrated because of the requirement for smaller and smaller components for electrical applications. By using micromechanical elements, such as micromechanical switches or microrelays, many advantages can be achieved. For example, the size of the devices becomes smaller and the manufacturing costs become lower. There are also other advantages as will be demonstrated later.
In the following micromechanical switches are presented more closely. Micromechanical switches belong to the field of micromechanical elements, which will be widely used in many future applications. Micromechanical switches create interesting opportunities, e.g. for radio frequency circuits. The advantages of using micromechanical structures, especially when applied to radio frequency circuits, are low insertion loss (below 0.5 dB) and high isolation (over 30 dB). A further advantage of micromechanical switches is that micromechanical switch structures can be integrated monolithically in integrated circuits. FIGS. 1a–c show three different commonly used basic structures of micromechanical switches. In FIG. 1a it is shown so called micromechanical cantilever switch. In FIG. 1b it is shown a micromechanical cantilever switch that connects sections of a transmission line. FIG. 1c illustrates a micromechanical bridge switch.
The operation of a micromechanical switch is controlled with a control signal or signals, coupled to electrodes of the switch. By means of the control signal the micromechanical switch is arranged to change its state. The main disadvantage of the currently available micromechanical switches operated by electrostatic or voltage control is that the necessary control voltage tends to be in the range of 10–30 V. This kind of voltage is much higher than the supply voltage used in state-of-the-art (Bi)CMOS devices used for switching operations. Furthermore, the switching delay and necessary control voltage level are fundamentally related to each other in that a faster switching time requires a higher mechanical resonance frequency and thus a stiffer mechanical structure. Stiffer mechanical structures will however make higher control voltage levels necessary.
3. The Theory of Switching Dynamics in Micromechanical Switches
In micromechanical elements, especially in micromechanical switches, the switching characteristics and behavior resembles classical mechanical relays in many senses. For this reason the operation of micromechanical switches are modeled with simplified piston models.
The electrostatic force between the capacitor plates of a plate capacitor is
                    F        =                              -                                          ∂                W                                            ∂                x                                              =                                                    -                                  ∂                                      ∂                    x                                                              ⁢                              (                                                      1                    2                                    ⁢                                      CU                    2                                                  )                                      =                                                                                -                                          ∂                                              ∂                        x                                                                              ⁢                                      (                                                                  Q                        2                                                                    2                        ⁢                        C                                                              )                                                  ⇔                                                                  ⁢                F                            =                                                                                          ɛ                      0                                        ⁢                                          AU                      2                                                                            2                    ⁢                                                                  (                                                                              g                            0                                                    -                          x                                                )                                            2                                                                      =                                                                            Q                      2                                                              2                      ⁢                                              ɛ                        0                                            ⁢                      A                                                        .                                                                                        (        1        )            
Here W is the energy stored in the capacitance C, U is the voltage difference, Q is the charge, x is the displacement, and go is the original gap between the capacitor plates.
In FIG. 2 is shown a simplified piston type model for a micromechanical switch. This consists of a mass, a spring, a damper, a plate capacitor structure, and optional insulating motion limiters 203. When an electrostatic force is applied between the fixed electrode 202 and the moving part 201 of the piston type structure, an electrostatic attractive force is created between the electrodes. A force balance between the mechanical spring force and the electrostatic force is created:
                                          ∑            F                    =                                                    F                electric                            +                              F                mechanical                                      =                                                                                                      ɛ                      0                                        ⁢                                          AU                      2                                                                            2                    ⁢                                                                  (                                                                              g                            0                                                    -                          x                                                )                                            2                                                                      -                                  κ                  ⁢                                                                          ⁢                  x                                            =              0                                      ,                            (        2        )            where g0 is the original gap between the capacitor plates, x is the displacement from the rest position, U is the electric potential difference between the capacitor plates, κ is the spring constant, A is the capacitor area, and ε0 is the dielectric constant.
The model of FIG. 2 is a good approximation of a voltage controlled micromechanical capacitor, switch or relay. The system is instable when the mechanical force cannot any longer sustain the electrical force. This will occur when both the sum of the forces (ΣF ) and the sum of the derivatives of the forces
  (            ∂              ∂        x              ⁢          (              ∑        F            )        )are zero.
The pull-in or the collapse of the piston structure occurs independently of the dimensions of the structure when the deflection isx=g0/3,  (3)and when the voltage is
                              U                      pull            ⁢                          -                        ⁢            in                          =                                                            8                ⁢                κ                ⁢                                                                  ⁢                                  g                  0                  3                                                            27                ⁢                                  ɛ                  0                                ⁢                A                                              .                                    (        4        )            
As can be seen from FIG. 2 insulating bumps 203 can be arranged on the electrode 202 to limit the minimum distance between the electrodes at pull-in.
After the collapse the gap is reduced to a value determined by the height hbump of these mechanical limiters on the surface of the fixed electrode. In order to release the switch, the voltage between the electrodes must be reduced to a value where the mechanical force can again compensate the electrical force. Thus we can find the value of the release voltage
                              U          release                =                                                            2                ·                κ                ·                                  (                                                            g                      0                                        -                                          h                      bump                                                        )                                ·                                  h                  bump                  2                                                                              ɛ                  0                                ⁢                A                                              .                                    (        5        )            
The release voltage is clearly smaller than the pull-in voltage. For example, for 100 nm high limiters, the release voltage is roughly 10% of the pull-in voltage. Thus even if a high voltage is needed for causing pull-in, a much lower voltage is needed to keep the electrode in the pulled-in state.
FIG. 3a illustrates the typical voltage-to-deflection characteristics of a micromechanical switch. The movable structure deflects towards the fixed electrode until the pull-in happens. When the voltage is lowered below the release voltage, the structure relaxes back to the equilibrium position between the mechanical and electrostatic forces. In general, structures with multiple states can be designed as well. FIG. 3b illustrates an example of a system with two different stable pull-in states, a first active (closed) state 306 and second active (closed) state 307.
Equation (1) implies that if the charge of the capacitor can be controlled instead of the voltage across the capacitor, the pull-in instability can be avoided because the force generated by a constant charge is not dependent on deflection. There are several implementations known in literature to achieve charge control, and charge control of micromechanical structures are experimentally proven. The advantage is a much larger tuning range.
Instead of constant voltage or constant charge, an AC voltage or current can as well be used to control the deflection of a micromechanical structure. When a sinusoidal current is applied through a capacitor, the charge of the capacitor q behaves as
                                          q            .                    =                                                                                          i                    ^                                    ac                                ⁢                sin                ⁢                                                                  ⁢                                  ω                  ac                                ⁢                t                            ⇒                                                          ⁢              q                        =                                                                                                      i                      ^                                        ac                                                        ω                    ac                                                  ⁢                                  (                                      1                    -                                          cos                      ⁢                                                                                          ⁢                                              ω                        ac                                            ⁢                      t                                                        )                                            +                              q                0                                                    ,                            (        6        )            where îac is the amplitude of the AC current and ωac is the frequency. For further analysis, the initial charge q0 can be set to zero. If the frequency of the AC current is higher than the mechanical resonance frequency, the dc component of the force will be
                              F          dc                ≈                                                            i                ^                            ac              2                                      2              ⁢                              ɛ                0                            ⁢                              Aω                ac                2                                              .                                    (        7        )            
One simple way to convert the AC voltage signal into an effective AC current is to use a LC tank circuit. Typically the capacitance of a micromechanical element is in the range from 1 pF to 30 pF. The AC voltage input signal is converted into an alternating current through the capacitor. With the help of an LC tank circuit very high amplitude of oscillating current or charge on the capacitor can be achieved. The amplitude of the current depends on the quality factor Q of the LC tank circuit when the tank circuit is resonating. In the preferred implementation, the tank circuit Q value should be over 10.
If the LC tank circuit is applied to switch control, the switching delay of a micromechanical element controlled by an AC signal passed through the inductor depends on several parameters:τswitch=τswitch(Qm, f0, Upull-in, Ucontrol, f1, Qs, fLC)  (8)where f0 is the mechanical resonance frequency, Qm the mechanical quality factor, Upull-in the pull-in voltage, fLC is the resonance frequency of the LC tank circuit at the initial state with no deflection of the micromechanical element, Qs the quality factor of the LC tank circuit, and Ucontrol and f1 are the level and frequency of the control voltage, respectively.
In order to optimize the switching delay, the mechanical quality factor needs to be compromised to be high enough to give sufficient fast motion but also small enough to damp the switch bouncing after first contact. Optimal value for the mechanical quality factor is roughly 0.05–0.5. This can be adjusted by suitable design of the switch structure and by the pressure of the surrounding gas.
The switching time is inversely proportional to the mechanical resonance frequency. The lower the required switching time, the stiffer the mechanical structure should be. According to Equation (3) this leads to a higher pull-in voltage and a higher voltage level needed to trigger the micromechanical bi-stable element.
The switching delay is also dependent on the amplitude and the frequency of the control signal. In addition, the matching between the tank circuit resonance frequency fLC and the control signal frequency f1 will influence the force and the switching delay. Note that the tank circuit resonance frequency fLC is not constant during the operation of the switch: when the capacitive gap of the micromechanical structure gets narrower, the resonance frequency fLC gets lower and is mismatched from the signal frequency f1.
FIG. 3c shows the dependence of the switching delay on the ratio between the electrical (fLC) or mechanical (fm) resonance frequencies to the signal frequency f1. The switching delay is shortened by increasing the signal frequency f1. The optimal signal frequency is 100–1000 times higher than the mechanical resonance frequency. FIG. 3d shows the dependence of the switching delay on the ratio between the tank circuit resonance frequency fLC and the control signal frequency f1. The minimal switching delay is achieved by setting the control signal frequency f1 roughly 1–3% lower than the initial tank circuit resonance frequency fLC.